///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
/// Permission is hereby granted, free of charge, to any person obtaining a copy
/// of this software and associated documentation files (the "Software"), to deal
/// in the Software without restriction, including without limitation the rights
/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
/// copies of the Software, and to permit persons to whom the Software is
/// furnished to do so, subject to the following conditions:
/// 
/// The above copyright notice and this permission notice shall be included in
/// all copies or substantial portions of the Software.
/// 
/// Restrictions:
///		By making use of the Software for military purposes, you choose to make
///		a Bunny unhappy.
/// 
/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
/// THE SOFTWARE.
///
/// @ref gtx_fast_trigonometry
/// @file glm/gtx/fast_trigonometry.inl
/// @date 2006-01-08 / 2014-11-25
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////////////////////

namespace glm {
    namespace detail {
        template<typename T>
        GLM_FUNC_QUALIFIER T
        cos_52s(T
        x) {
        T const xx(x *x);

        return (T(0.9999932946) +
        xx *(T(-0.4999124376)
        +
        xx *(T(0.0414877472)
        +
        xx *T(-0.0012712095)
        )));
    }

    template<typename T, precision P, template<typename, precision> class vecType>
    GLM_FUNC_QUALIFIER vecType<T, P>
    cos_52s(vecType<T, P>
    const & x) {
    return
    detail::functor1<T, T, P, vecType>::call(cos_52s, x
    );
}
}//namespace detail

// wrapAngle
template<typename T>
GLM_FUNC_QUALIFIER T
wrapAngle(T
angle)
{
return
abs<T>(mod<T>(angle, two_pi<T>())
);
}

template<typename T, precision P, template<typename, precision> class vecType>
GLM_FUNC_QUALIFIER vecType<T, P>
wrapAngle(vecType<T, P>
const & x)
{
return
detail::functor1<T, T, P, vecType>::call(wrapAngle, x
);
}

// cos
template<typename T>
GLM_FUNC_QUALIFIER T
fastCos(T
x)
{
T const angle(wrapAngle < T > (x));

if(angle<half_pi<T>())
return
detail::cos_52s(angle);
if(angle<pi<T>())
return -

detail::cos_52s (pi<T>()

- angle);
if(angle<(T(3) *

half_pi<T>()

))
return -
detail::cos_52s(angle
-

pi<T>()

);

return

detail::cos_52s (two_pi<T>()

- angle);
}

template<typename T, precision P, template<typename, precision> class vecType>
GLM_FUNC_QUALIFIER vecType<T, P>
fastCos(vecType<T, P>
const & x)
{
return
detail::functor1<T, T, P, vecType>::call(fastCos, x
);
}

// sin
template<typename T>
GLM_FUNC_QUALIFIER T
fastSin(T
x)
{
return

fastCos <T> (half_pi<T>()

- x);
}

template<typename T, precision P, template<typename, precision> class vecType>
GLM_FUNC_QUALIFIER vecType<T, P>
fastSin(vecType<T, P>
const & x)
{
return
detail::functor1<T, T, P, vecType>::call(fastSin, x
);
}

// tan
template<typename T>
GLM_FUNC_QUALIFIER T
fastTan(T
x)
{
return x + (
x *x
*
x *T(0.3333333333)
) + (
x *x
*
x *x
*
x *T(0.1333333333333)
) + (
x *x
*
x *x
*
x *x
*
x *T(0.0539682539)
);
}

template<typename T, precision P, template<typename, precision> class vecType>
GLM_FUNC_QUALIFIER vecType<T, P>
fastTan(vecType<T, P>
const & x)
{
return
detail::functor1<T, T, P, vecType>::call(fastTan, x
);
}

// asin
template<typename T>
GLM_FUNC_QUALIFIER T
fastAsin(T
x)
{
return x + (
x *x
*
x *T(0.166666667)
) + (
x *x
*
x *x
*
x *T(0.075)
) + (
x *x
*
x *x
*
x *x
*
x *T(0.0446428571)
) + (
x *x
*
x *x
*
x *x
*
x *x
*
x *T(0.0303819444)
);// + (x * x * x * x * x * x * x * x * x * x * x * T(0.022372159));
}

template<typename T, precision P, template<typename, precision> class vecType>
GLM_FUNC_QUALIFIER vecType<T, P>
fastAsin(vecType<T, P>
const & x)
{
return
detail::functor1<T, T, P, vecType>::call(fastAsin, x
);
}

// acos
template<typename T>
GLM_FUNC_QUALIFIER T
fastAcos(T
x)
{
return T(1.5707963267948966192313216916398) -
fastAsin(x); //(PI / 2)
}

template<typename T, precision P, template<typename, precision> class vecType>
GLM_FUNC_QUALIFIER vecType<T, P>
fastAcos(vecType<T, P>
const & x)
{
return
detail::functor1<T, T, P, vecType>::call(fastAcos, x
);
}

// atan
template<typename T>
GLM_FUNC_QUALIFIER T
fastAtan(T
y,
T x
)
{
T sgn = sign(y) * sign(x);
return
abs(fastAtan(y / x)
) *
sgn;
}

template<typename T, precision P, template<typename, precision> class vecType>
GLM_FUNC_QUALIFIER vecType<T, P>
fastAtan(vecType<T, P>
const & y,
vecType<T, P> const &x
)
{
return
detail::functor2<T, P, vecType>::call(fastAtan, y, x
);
}

template<typename T>
GLM_FUNC_QUALIFIER T
fastAtan(T
x)
{
return x - (
x *x
*
x *T(0.333333333333)
) + (
x *x
*
x *x
*
x *T(0.2)
) - (
x *x
*
x *x
*
x *x
*
x *T(0.1428571429)
) + (
x *x
*
x *x
*
x *x
*
x *x
*
x *T(0.111111111111)
) - (
x *x
*
x *x
*
x *x
*
x *x
*
x *x
*
x *T(0.0909090909)
);
}

template<typename T, precision P, template<typename, precision> class vecType>
GLM_FUNC_QUALIFIER vecType<T, P>
fastAtan(vecType<T, P>
const & x)
{
return
detail::functor1<T, T, P, vecType>::call(fastAtan, x
);
}
}//namespace glm
